Prime Minister Jacinda Ardern has issued a stark warning to international visitors coming to New Zealand, saying they will be quarantined and possibly deported if they refuse to self-isolate.

New Zealand's strict travel restrictions, meaning anyone entering the country except from the Pacific must self-isolate for 14 days, began at 1am this morning.

Those arriving at airports are filling in forms to register where they've been and where they are residing, and talking to a nurse to be talked through self-isolation requirements.

Ardern said more than 10,000 New Zealanders have self-isolated so far and have been compliant, and international visitors should do the same.

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"If they do not self isolate, I will have them quarantined. And I am looking at my deportation powers," she told Newstalk ZB this morning.

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The new system at airports had just been put in place and Ardern said she couldn't guarantee that everyone was getting a one-on-one debrief about self-isolation.

"But we absolutely should have all of their details."

Yesterday she said New Zealanders who were not self-isolating properly could be forced by police into a medical facility, with staff stationed at the doors - though these powers had not been used so far.

This comes as the Reserve Back this morning cut the Official Cash Rate to a record low 0.25 per cent, while Cabinet later today will flesh out the details of its economic response to help tens of thousands of workers to stay in jobs and thousands of businesses to survive.

Ardern said the package, to be announced tomorrow, would be the most significant one she would make as Prime Minister, but wouldn't be drawn on how much it would cost or whether it would be more than the $12b infrastructure announcement she made earlier this year.

"It will be a multi-billion dollar package. It will be very significant because it needs to be."

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She expected to release guidelines around public gatherings later this week, but events that see people in close proximity in a way that they cannot be traced are likely to be cancelled.

"There is an inevitability there that we'll be telling you you can't go there," Ardern said.

That might include music festivals Homegrown and CubaDupa in Wellington in the coming weeks.

Ardern said the Government was closely following the successful model in Taiwan, and that was partly why New Zealand had not closed schools

Another reason was because children are less susceptible to Covid-19 infection, and closing a school might put them in more contact with older people, such as a grandparent, who are more at risk of infection and death.

She asked schools that were considering closing their doors to listen to the advice of the Government.

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"We have all of the evidence, we are basing every decision on that, and we have no hesitation being bold. We are going hard and early."

She said testing capacity should soon reach 1500 tests per day - with more capacity on the way - and there was no reason for clinicians to hesitate in asking people to get tested.

"You're the ones to make that judgement and err on the side of caution."

The eighth Covid-19 case in New Zealand was officially confirmed yesterday, after a Danish tourist in her 30s touched down in Auckland via Doha on March 10.

She then flew on a Jetstar flight to Christchurch before driving to Queenstown, where she is now in hospital after becoming ill.

The seventh coronavirus case was also confirmed by health authorities yesterday - a man from Australia who arrived in Wellington on Saturday morning from Brisbane on an Air New Zealand flight.

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Authorities said he was now in self-isolation with his partner and another family member. He is not in hospital.

As of 7am, the latest figures show that almost 160,000 people around the world have been infected. The death toll is now just past 6000.

There have been no deaths in New Zealand to date.